HEPTAGONAL numbers, are a sort of polygonal numbers, wherein the difference of the terms of the corresponding arithmetical progression is = 5. One of the properties of these numbers is, that if they be multiplied by 40, and 9 be added to the product, the sum is a square number.

HEPTARCHY, a government which consisted of 7 kings or sovereign princes. Such was the government under which England was ruled by the Saxon kings.

HERALD, an officer at arms, whose duty is to declare war, to proclaim peace, or to be employed in martial messages. The heralds in England are judges and examiners of that ridiculous jargon called heraldry, or coats of arms; they marshal all solemnities at the coronations, and funerals of their princes, &c. The origin of heralds is extremely ancient. It is reported that the Greek herald, Stentor, possessed such a powerful voice that it exceeded the united clamor of fifty men.

There are three heralds called kings at arms in England, each bearing a name peculiar to himself, and six heralds. The first king at arms is that of Garter, created by Henry V., that of Clarencieux, created by Edward IV. and that of Norroy, so called from the exercise of his functions north of the river Trent.

The heralds extraordinary are those of Windsor and Chester, created by Edward III., those of Somerset by Henry VIII. and those of York and Lancaster, created by the children of Edward III. They are pageants and sinecures.

HERALDS College, a corporation in England which consists of kings at arms, heralds, and pursuivants, in which the nonsense of heraldry is recorded.

HERAUT, Fr. herald. During the old monarchy of France there were thirty heralds each distinguished by the name of some particular province. The first of these who was king at arms, bore the title of Montjoy St. Denis: he had the privilege of wearing a royal coronet over the fleur de luce. On solemn occasions the king and the heralds at arms appeared in their coats of arms made of violet colored crimson velvet, with three golden fleurs de luces before and behind, and as many on each sleeve where the name of the province stood, to which the herald belonged. They wore a black velvet cap ornamented with golden strings, and half boots, when they appeared on peaceable occasions, with whole boots on warlike or martial ones. In solemn funerals they had a long robe of black velvet. The only difference between the king at arms and the heralds with respect to dress, consisted in the richness of the embroidery, that of the former being more expensive. The coats of arms which were peculiar to the heralds were called Plaques, those of the kings at arms were distinguished by the name of Tunics. They carried a stick called Caduceus (such as Mercury is represented to have borne in ancient mythology.) But this stick was not ornamented by a crown with fleurs de luce, it was only covered with crimson velvet, having a few fleurs de luce scattered here and there.

There was likewise a herald, whose particular functions were to carry the king’s orders. He was entitled to a coat of arms upon violet colored velvet, interspersed with fleurs de luce and gold embroidered flammes or pendants, together with the arms and collars both before and behind. He likewise wore the cross belonging to the order which was attached to a black silk cord borne cross-ways.

The author of the Dictionnaire Militaire derives the French term Heraut from the German Hérald, which signifies a man at arms, un Gendarme. Verstegan derives it from the Saxon. Other French writers derive it from an old Gallic word harou, or hara, which was used as a challenge, a notification of fresh hostilities, a ban or general assembling of the people, a loud and public proclamation of battles fought and victories obtained; on which account heralds, according to Ducange, were formerly called Clarigarvis as well as Heraldus.

HERCOTECTONIQUE, Fr. a term in fortification signifying that branch of Military architecture which specifically points out the best means of defence and the surest method of providing stores. This word is derived from the Greek.